Superconducting and Normal Specific Heats of a Single Crystal of Niobium

Abstract

The anomalous specific heat found in a polycrystalline sample of niobium and previously reported from this laboratory by Hirshfeld, Leupold, and Boorse (HLB) prompted complete remeasurements both in the normal and superconducting phases on a single crystal with lower tantalum content. The thermal constants of the single crystal show only small differences from the polycrystal in the same temperature range, the single-crystal values being ${T}_{c}=9.20\ifmmode^\circ\else\textdegree\fi{}$K and $\ensuremath{\bigominus}=241\ifmmode^\circ\else\textdegree\fi{}$K between about 10\ifmmode^\circ\else\textdegree\fi{} and 3\ifmmode^\circ\else\textdegree\fi{}K. The normal-state single-crystal measurements agree with measurements on the HLB polycrystal made both in this laboratory and by van der Hoeven and Keesom at Purdue University. The latter measurements were carried to about 0.4\ifmmode^\circ\else\textdegree\fi{}K in a field of 17 kG. As a result of their investigation, they report a Debye \ensuremath{\bigominus} of 275\ifmmode^\circ\else\textdegree\fi{}K in the region below 3\ifmmode^\circ\else\textdegree\fi{}K. With this value of \ensuremath{\bigominus}, the anomaly in the specific heat disappears. As both the single-crystal results and the van der Hoeven and Keesom values agree in the mutually measured ranges, \ensuremath{\bigominus} is taken to be 275\ifmmode^\circ\else\textdegree\fi{}K. The corresponding value of $\ensuremath{\gamma}$ is found to be 7.80 mJ/mole ${\mathrm{deg}}^{2}$. The usual exponential behavior of the electronic specific heat $\frac{{C}_{\mathrm{es}}}{\ensuremath{\gamma}{T}_{c}}=a{e}^{\ensuremath{-}\frac{b{T}_{c}}{T}}$ with $a=8.21$ and $b=1.52$, is observed over a restricted temperature range. Below $t=5$ the data exhibit larger values than predicted by the exponential in agreement with a number of other superconductors. The value of the energy gap at 0\ifmmode^\circ\else\textdegree\fi{}K was found to be $3.69 k{T}_{c}$. Overall comparisons are made with the BCS theory and a modification due to Swihart.